Linganisha mbinu

	Modeli wa Soko wa Libor	Uthamini Usio na Hatari (Risk-Neutral Valuation)
Nyanja	Fedha za Kiidadi	Fedha za Kiidadi
Familia	Regression model	Regression model
Mwaka wa asili	1997	1979
Mwanzilishi	Alan Brace, Dariusz Gatarek, and Marek Musiela	John Harrison and David Kreps
Aina	Interest Rate Model	Fundamental Principle
Chanzo asilia	Brace, A., Gatarek, D., & Musiela, M. (1997). The market model of interest rate dynamics. Mathematical Finance, 7(2), 127-155.	Harrison, J. M., & Kreps, D. M. (1979). Martingales and arbitrage in multiperiod securities markets. Journal of Economic Theory, 20(3), 381-408.
Majina mbadala	BGM Model, LMM	Risk-Neutral Measure, Q-Measure
Zinazohusiana	4	4
Muhtasari	The LIBOR Market Model (BGM), developed by Brace, Gatarek, and Musiela (1997), is a multi-factor interest rate model that directly models forward LIBOR rates as lognormal processes. Unlike short-rate models, LMM naturally prices caplets at the market level and is the industry standard for valuing caps, floors, and exotic interest rate derivatives.	Risk-neutral valuation (1979) is the fundamental principle that derivative prices equal the expected payoff discounted at the risk-free rate, computed under a risk-neutral probability measure (Q-measure). This principle, formalized by Harrison and Kreps, eliminates the need to estimate risk premia and is the foundation of modern derivatives pricing.